5-9 A pump increases the water pressure from 70 kPa at the inlet to 700 kPa at t

Question

5-9 A pump increases the water pressure from 70 kPa at the inlet to 700 kPa at the outlet. Water enters this pump at 15 degree Celsius through a 1-cm-diameter opening and exists through a 1.5-cm-diameter opening. Determine the velocity of the water at the inlet and outlet when the mass flow rate through the pump is 0.5 kg/s. Will these velocities change significantly if the inlet temperature is raised to 40 degree Celsius?
(note: why does the solution on Chegg/Cramster; have v1 =vf. Also how do we know that mass flow rate remains constant?)

Explanation / Answer

mass flow is constant as what goes in comes out
consider mass as particles so number of particles going it the pump comes out of the pump so mass flow is constant
1*A1*v1 = 2*A2*v2 = 0.5 kg/s

(3.14*1^2*10^-4/4)*v1*(1/0.001036) = 0.5

v1 = 6.6 m/s

(3.14*1.5^2*10^-4/4)*v2*(1/0.001108) = 0.5

v2 = 3.13 m/s

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